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What is the sum of four angles if two are complementary and two are supplementary?

(A)
180 degrees

(B)
360 degrees

(C)
270 degrees

(D)
90 degrees

How many noncolinear points are required to determine a plane?

(A)
Two

(B)
An infinite number

(C)
Four

(D)
Three

How many dimensions are spanned by intersecting lines?

(A)
Two

(B)
Three

(C)
One

(D)
More information is needeed

How many times can two lines intersect?

(A)
Zero

(B)
One

(C)
Two

(D)
Zero or One

When is a line l perpendicular to a plane?

(A)
When l and the plane intersect at one point

(B)
When l and the plane don't intersect

(C)
When every line in the plane that contains the intersection point of the l and the
plane is perpendicular to l

(D)
When l intersects evey line in the plane at a 90 degree angle

Which of the following figures is two-dimensional?

(A)
A ray

(B)
A polygon

(C)
A point

(D)
A sphere united with its interior points

Which of the following angles must be an exterior angle?

(A)
A 120 degree angle

(B)
An angle whose complement is 75 degrees

(C)
A right angle

(D)
A 230 degree angle

Adjacent angles can be all but which of the following?

(A)
Complementary

(B)
Vertical

(C)
Acute

(D)
Supplementary

When two lines intersect, they form two pairs of what?

(A)
Vertical angles

(B)
Adjacent angles

(C)
Supplementary angles

(D)
Right Angles

Angles ABC and DBE are which of the following?

Figure 1

(A)
Vertical

(B)
Complementary

(C)
Supplementary

(D)
Vertical and supplementary

There exists a line l and two distinct points not on l. How many lines
parallel to l can be drawn containing those two points?

(A)
One

(B)
Two

(C)
Zero

(D)
Either zero or one; it depends on the locations of the points.

Given that lines l and m are parallel, what is the measure of angle 1?

Figure 2

(A)
30 degrees

(B)
60 degrees

(C)
120 degrees

(D)
Impossible to Calculate

When a transversal cuts three parallel lines, how many pairs of supplementary angles are
formed?

(A)
12

(B)
18

(C)
24

(D)
36

If line l bisects angle ABC, what is the measure of angle 1?

Figure 3

(A)
110 degrees

(B)
70 degrees

(C)
55 degrees

(D)
35 degrees

The distance from a point to a line is what?

(A)
The length of any segment drawn between the point and the line

(B)
The length of another line perpendicular to the first line, containing the point

(C)
The length of the segment perpendicular to the line with one endpoint at the point and
one endpoint on the line

(D)
Any of the above -- they're all the same

How many lines can be drawn that are oblique to a given line?

(A)
An infinite number

(B)
One

(C)
Zero

(D)
Not enough information to tell

What can you conclude about two lines if the pairs of vertical angles created at their
intersection are supplementary?

(A)
The lines are parallel

(B)
The lines are perpendicular

(C)
The lines are oblique

(D)
Nothing

How many midpoints does a segment have?

(A)
Zero

(B)
One

(C)
An infinite number

(D)
Not enough information to tell

When a straight angle is bisected, two angles are formed. What can be said about these
angles?

(A)
They are supplementary

(B)
They are adjacent

(C)
They are right

(D)
All of the above

If a right angle is bisected, and one of the new angles formed by the bisector is trisected,
what is the measure of one of the three newest angles?

(A)
30 degrees

(B)
22.5 degrees

(C)
15 degrees

(D)
10 degrees

If the starting point of a curve is the same as its ending point, what is the curve called?

(A)
A simple closed curve

(B)
A polygon

(C)
A surface

(D)
A closed curve

The following figure is which of the following?

Figure 4

(A)
A closed curve

(B)
A simple closed curve

(C)
A polygon

(D)
Either a closed curve or a simple closed curve

What is the greatest number of interior diagonals a concave pentagon can have?

(A)
Three

(B)
Four

(C)
Five

(D)
Zero

If a quadrilateral and a traingle share one side, what is the name of the polygon created by
their union?

(A)
Hexagon

(B)
Heptagon

(C)
Quadrilateral

(D)
Their union doesn't necessarily result in a polygon

If the sum of the exterior angles of a polygon equals 360 degrees, how many sides does
the polygon have?

(A)
Four

(B)
Three

(C)
More than six

(D)
Not enough information to tell

Which of the following polygons is always convex?

(A)
A triangle

(B)
A quadrilateral

(C)
A pentagon

(D)
A dodecagon

How many triangles must be combined to assemble a heptagon?

(A)
Two

(B)
Three

(C)
Five

(D)
Triangles cannot be combined to form a heptagon

If the interior angles of a polygon sum to 720 degrees, how many vertices does that
polygon have?

(A)
Four

(B)
Five

(C)
Six

(D)
The sum of the interior angles of a polygon never equals 720 degrees

A rectangle is an example of what?

(A)
An equilateral polygon

(B)
A parallelogram

(C)
A closed curve

(D)
Answers (b) and (c)

Given that the quadrilateral pictured is a parallelogram, what is the measure of angle 1?

Figure 5

(A)
30 degrees

(B)
60 degrees

(C)
150 degrees

(D)
Not enough information to tell

Given that the quadrilateral pictured is a parallelogram, what is the measure of angle 2?

Figure 6

(A)
40 degrees

(B)
80 degrees

(C)
100 degrees

(D)
Not enough information to tell

What polygon has 540 degrees of interior angles and 14 diagonals?

(A)
A pentagon

(B)
A heptagon

(C)
Any polygon

(D)
There is no polygon with such characteristics

If the sum of the lengths of the bases of a trapezoid is 12, what is the length of its
median?

(A)
12

(B)
6

(C)
4

(D)
8

If a central angle is 35 degrees, what is the measure of the major arc whose endpoints are
the intersection points of the central angle and the circle?

(A)
35 degrees

(B)
145 degrees

(C)
325 degrees

(D)
395 degrees

The radius of a circle is 14. How long is the chord whose endpoints are the same as the
endpoints of a 180 degree arc?

(A)
7

(B)
14

(C)
28

(D)
Not enough information

If a sector is partially bound by the diameter of a circle, what is the measure of the arc
that completes the boundary of the sector?

(A)
360 degrees

(B)
180 degrees

(C)
90 degrees

(D)
270 degrees

Which of the following sets of figures do not determine a circle?

(A)
A center and a diameter

(B)
A center and a secant line

(C)
A diameter and a tangent line

(D)
A center and a chord

If a secant line contains the center of a circle as well as the midpoint of a chord of the
circle, and these two points are different, what is the relationship between the secant line
and the chord?

(A)
The secant line and the line that contains the chord are parallel.

(B)
The secant line contains the chord.

(C)
The secant line is the perpendicular bisector of the chord.

(D)
There is no special relationship between the secant line and the chord.

The angle created by a tangent line and the radius of a circle whose endpoint is the point
of tangency is bisected. What is the measure of the two new angles created?

(A)
90 degrees

(B)
180 degrees

(C)
45 degrees

(D)
30 degrees

A hexagon is circumscribed about a circle. How many radii can be drawn that are
perpendicular to a side of the hexagon?

(A)
Zero

(B)
Five

(C)
Six

(D)
12

How many curves exist in a surface?

(A)
Zero

(B)
One

(C)
However many dimensions the surface has

(D)
An infinite number

The bases of a prism are octagons. How many lateral edges are there in the prism?

(A)
Four

(B)
Eight

(C)
Twelve

(D)
Sixteen

The lateral faces of a prism could be which of the following?

(A)
Parallelograms

(B)
Squares

(C)
Rhombuses

(D)
Any of the above

If planes are oblique, what is their intersection?

(A)
A point

(B)
A line

(C)
A plane

(D)
A segment

Which of the following is not necessarily a convex simple closed surface?

(A)
A cone

(B)
A polyhedron

(C)
A pyramid

(D)
A right prism

At how many points can a line and a surface intersect?

(A)
Zero

(B)
One

(C)
Three

(D)
They can intersect at an infinite number of points.

What is the least number of polygons needed to form the surface of a polyhedron?

(A)
One

(B)
Two

(C)
Three

(D)
Four

When does the altitude of a pyramid lie within one of the faces of the pyramid?

(A)
When the pyramid is a regular pyramid

(B)
Only when the altitude is one of the lateral edges of the pyramid

(C)
When a line can be drawn that is perpendicular to the plane of the base and contains the
vertex as well as a point on the polygon that bounds the base

(D)
Only when the base of the pyramid is a triangle

When are two planes perpendicular?

(A)
When one plane contains a line which is perpendicular to the other plane

(B)
When their intersection is a line

(C)
When every line in one plane is perpendicular to every line in the other plane

(D)
When any given third plane either intersects both planes or neither

When spheres intersect one another, their intersection could be